Quite a few years ago I put Nylguts on a Vega style N banjo. I don't remember the gauges, but I did research the strings on an online string calculator to get the proper tension. I was very disappointed with the results. The voice was weak, & uninteresting, & I went back to steel strings which made a world of difference.

IMO you’d be better off by building a set from high-tension nylon guitar strings. You may also find you need to play close to the bridge for the strings to have enough tension to perform well with a flat pick. You’ll need to experiment with gauges though.

I would start with a baritone uke set. They're pretty close to the same scale length. Typical tuning is different but it would be a start. The 3rd probably ought to be wound. Any of the online calculators will get you in the ballpark.

I'd also go with a very light bridge. Softwoods like pine work well with nylon.

I sometimes fingerpick my tenors, so nylon would be easier on the fingers. Ought to be a fun experiment. Keep us posted!

I did the same thing Marc Smith did with a set of baritone uke strings. They worked well enough when I tuned it to DGBE like a baritone uke. If you want to experiment with other tunings, they probably won't be ideal. The banjo I had was a 17 fret open back, and I wasn't exactly overwhelmed by the sound, but it was fun to play around with. I finally got bored and went back to steel strings.

Did this years ago with a tenor banjo when I was playing with some folks from Ireland and the sessions didn't have a banjo player. I simply bought D, G, B and E classical guitar strings and put them on. Worked fine

Many are stringing 20” baritone ukes with the Aquila 31U strings. Whether they are long enough for a 22” tenor including the tailpiece is something I just don’t know. I could put a set on my next stock order and try to fit them to my 23" Kay if you aren't in a hurry.

At that scale, they can be tuned up to CGDA or down to GDAE. “Mellow” is not a word that I use to describe banjo ukuleles that I have tuned CGDA with these. Nylgut strings have quite a bit of stretch to them as long as there are no burrs or tears in the polymer. Any nick and it's like scratching glass. Nylon is far more robust in that regards but the tone is a lot softer. 

Thanks to all for your advice and suggestions. Since my original post I have watched a youtube video of a tenor banjo with nylon (maybe Nylgut?) strings being played. On the video it did sound okay. In the Comments the player wrote that he used Aquila Classic Minstrel Banjo strings. (I think that is correct but I'll look for that video again to be sure.) I searched for those strings and all the results were for the 5 string banjo which makes sense since Classic Banjo is 5 string.

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Originally posted by malarz

Thanks to all for your advice and suggestions. Since my original post I have watched a youtube video of a tenor banjo with nylon (maybe Nylgut?) strings being played. On the video it did sound okay. In the Comments the player wrote that he used Aquila Classic Minstrel Banjo strings. (I think that is correct but I'll look for that video again to be sure.) I searched for those strings and all the results were for the 5 string banjo which makes sense since Classic Banjo is 5 string.

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That's actually 7 different sets in my catalog, most of which I carry. I will recommend is the 7B set since it has a metal wound 4th string. Ignore the recommended pitches as NylGut will stretch over a wide range. One would have go with individual strings to do better. You can tune up to CGDA or down to GDAE — volume will change but it won't be too bad seeing as you have a 22" scale. I charge $11 for the set plus $2.50 postage in the US.

My favorite setup for 17fret GDAE was steel strings for 1 & 2 (a/e) and hard tension classical guitar wound E and A strings for the G and D. I think the steel strings were maybe gauges 10 and 20. I’ve done that on an old Orpheum and an old Vega Tubaphone and both sounded great. Neither one I still have though. I think they were more like 21” scale though. 22” seems long for a 17-fret, unless it’s on a large pot

I checked the scale length and it is 21". Sorry for my error. Interesting that tdennis didn't like the sound of his Vega with Nylgut strings. I found a video and the strings and banjo seems to sound fine. If you read his comments you see that he had to buy strings from different sets.

youtu.be/7PZl6hYrQGo?si=109g5cr6Z4b5831J